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A new and practical influence measure for subsets of covariance matrix sample principal components with applications to high dimensional datasets

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  • Prendergast, Luke A.
  • Li Wai Suen, Connie

Abstract

Principal Component Analysis (PCA) is an important tool in multivariate analysis, in particular when faced with high dimensional data. There has been much done with regard to sensitivity analysis and the development of influence diagnostics for the eigenvector estimators that define the sample principal components. However, little, if any, has been done in this setting with regard to the sample principal components themselves. In this paper we develop a sensitivity measure for principal components associated with the covariance matrix that is very much related to the influence function (Hampel, 1974). This influence measure is based on the average squared canonical correlation and differs from the existing measures in that it assesses the influence of certain observational types on the sample principal components. We use this measure to derive an influence diagnostic that satisfies two key criteria being (i) it detects influential observations with respect to subsets of sample principal components and (ii) is efficient to calculate even in high dimensions. We use several microarray datasets to show that our measure satisfies both criteria.

Suggested Citation

  • Prendergast, Luke A. & Li Wai Suen, Connie, 2011. "A new and practical influence measure for subsets of covariance matrix sample principal components with applications to high dimensional datasets," Computational Statistics & Data Analysis, Elsevier, vol. 55(1), pages 752-764, January.
    • Handle: RePEc:eee:csdana:v:55:y:2011:i:1:p:752-764
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    1. Ash A. Alizadeh & Michael B. Eisen & R. Eric Davis & Chi Ma & Izidore S. Lossos & Andreas Rosenwald & Jennifer C. Boldrick & Hajeer Sabet & Truc Tran & Xin Yu & John I. Powell & Liming Yang & Gerald E, 2000. "Distinct types of diffuse large B-cell lymphoma identified by gene expression profiling," Nature, Nature, vol. 403(6769), pages 503-511, February.
    2. Harrison, David Jr. & Rubinfeld, Daniel L., 1978. "Hedonic housing prices and the demand for clean air," Journal of Environmental Economics and Management, Elsevier, vol. 5(1), pages 81-102, March.
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    Cited by:

    1. Prendergast, Luke A. & Smith, Jodie A., 2022. "Influence functions for linear discriminant analysis: Sensitivity analysis and efficient influence diagnostics," Journal of Multivariate Analysis, Elsevier, vol. 190(C).
    2. Jacques Bénasséni, 2018. "A correction of approximations used in sensitivity study of principal component analysis," Computational Statistics, Springer, vol. 33(4), pages 1939-1955, December.

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